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<li><a class="reference internal" href="#">Probability Calibration for 3-class classification</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-calibration-plot-calibration-multiclass-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="probability-calibration-for-3-class-classification">
<span id="sphx-glr-auto-examples-calibration-plot-calibration-multiclass-py"></span><h1>Probability Calibration for 3-class classification<a class="headerlink" href="#probability-calibration-for-3-class-classification" title="Permalink to this headline">¶</a></h1>
<p>This example illustrates how sigmoid calibration changes predicted
probabilities for a 3-class classification problem. Illustrated is the
standard 2-simplex, where the three corners correspond to the three classes.
Arrows point from the probability vectors predicted by an uncalibrated
classifier to the probability vectors predicted by the same classifier after
sigmoid calibration on a hold-out validation set. Colors indicate the true
class of an instance (red: class 1, green: class 2, blue: class 3).</p>
<p>The base classifier is a random forest classifier with 25 base estimators
(trees). If this classifier is trained on all 800 training datapoints, it is
overly confident in its predictions and thus incurs a large log-loss.
Calibrating an identical classifier, which was trained on 600 datapoints, with
method=’sigmoid’ on the remaining 200 datapoints reduces the confidence of the
predictions, i.e., moves the probability vectors from the edges of the simplex
towards the center. This calibration results in a lower log-loss. Note that an
alternative would have been to increase the number of base estimators which
would have resulted in a similar decrease in log-loss.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="c1"># Author: Jan Hendrik Metzen &lt;jhm@informatik.uni-bremen.de&gt;</span>
<span class="c1"># License: BSD Style.</span>


<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_blobs</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.calibration</span> <span class="kn">import</span> <span class="n">CalibratedClassifierCV</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">log_loss</span>

<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

<span class="c1"># Generate data</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_blobs</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">cluster_std</span><span class="o">=</span><span class="mf">5.0</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="mi">600</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">600</span><span class="p">]</span>
<span class="n">X_valid</span><span class="p">,</span> <span class="n">y_valid</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="mi">600</span><span class="p">:</span><span class="mi">800</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="mi">600</span><span class="p">:</span><span class="mi">800</span><span class="p">]</span>
<span class="n">X_train_valid</span><span class="p">,</span> <span class="n">y_train_valid</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="mi">800</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">800</span><span class="p">]</span>
<span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="mi">800</span><span class="p">:],</span> <span class="n">y</span><span class="p">[</span><span class="mi">800</span><span class="p">:]</span>

<span class="c1"># Train uncalibrated random forest classifier on whole train and validation</span>
<span class="c1"># data and evaluate on test data</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">25</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_valid</span><span class="p">,</span> <span class="n">y_train_valid</span><span class="p">)</span>
<span class="n">clf_probs</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">score</span> <span class="o">=</span> <span class="n">log_loss</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">clf_probs</span><span class="p">)</span>

<span class="c1"># Train random forest classifier, calibrate on validation data and evaluate</span>
<span class="c1"># on test data</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">25</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">clf_probs</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">sig_clf</span> <span class="o">=</span> <span class="n">CalibratedClassifierCV</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s2">&quot;sigmoid&quot;</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="s2">&quot;prefit&quot;</span><span class="p">)</span>
<span class="n">sig_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_valid</span><span class="p">,</span> <span class="n">y_valid</span><span class="p">)</span>
<span class="n">sig_clf_probs</span> <span class="o">=</span> <span class="n">sig_clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">sig_score</span> <span class="o">=</span> <span class="n">log_loss</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">sig_clf_probs</span><span class="p">)</span>

<span class="c1"># Plot changes in predicted probabilities via arrows</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;r&quot;</span><span class="p">,</span> <span class="s2">&quot;g&quot;</span><span class="p">,</span> <span class="s2">&quot;b&quot;</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">clf_probs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="n">clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
              <span class="n">sig_clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
              <span class="n">sig_clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">clf_probs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
              <span class="n">color</span><span class="o">=</span><span class="n">colors</span><span class="p">[</span><span class="n">y_test</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span> <span class="n">head_width</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">)</span>

<span class="c1"># Plot perfect predictions</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">],</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Class 1&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">],</span> <span class="s1">&#39;go&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Class 2&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">],</span> <span class="s1">&#39;bo&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Class 3&quot;</span><span class="p">)</span>

<span class="c1"># Plot boundaries of unit simplex</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Simplex&quot;</span><span class="p">)</span>

<span class="c1"># Annotate points on the simplex</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($\frac</span><span class="si">{1}{3}</span><span class="s1">$, $\frac</span><span class="si">{1}{3}</span><span class="s1">$, $\frac</span><span class="si">{1}{3}</span><span class="s1">$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="o">.</span><span class="mi">23</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">],</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($\frac</span><span class="si">{1}{2}</span><span class="s1">$, $0$, $\frac</span><span class="si">{1}{2}</span><span class="s1">$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">0</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($0$, $\frac</span><span class="si">{1}{2}</span><span class="s1">$, $\frac</span><span class="si">{1}{2}</span><span class="s1">$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">0</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($\frac</span><span class="si">{1}{2}</span><span class="s1">$, $\frac</span><span class="si">{1}{2}</span><span class="s1">$, $0$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">6</span><span class="p">,</span> <span class="o">.</span><span class="mi">6</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($0$, $0$, $1$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($1$, $0$, $0$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;($0$, $1$, $0$)&#39;</span><span class="p">,</span>
             <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">xycoords</span><span class="o">=</span><span class="s1">&#39;data&#39;</span><span class="p">,</span>
             <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">),</span>
             <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="c1"># Add grid</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]:</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">],</span> <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Change of predicted probabilities after sigmoid calibration&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Probability class 1&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Probability class 2&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>

<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Log-loss of&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot; * uncalibrated classifier trained on 800 datapoints: </span><span class="si">%.3f</span><span class="s2"> &quot;</span>
      <span class="o">%</span> <span class="n">score</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot; * classifier trained on 600 datapoints and calibrated on &quot;</span>
      <span class="s2">&quot;200 datapoint: </span><span class="si">%.3f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">sig_score</span><span class="p">)</span>

<span class="c1"># Illustrate calibrator</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="c1"># generate grid over 2-simplex</span>
<span class="n">p1d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
<span class="n">p0</span><span class="p">,</span> <span class="n">p1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">p1d</span><span class="p">,</span> <span class="n">p1d</span><span class="p">)</span>
<span class="n">p2</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">p0</span> <span class="o">-</span> <span class="n">p1</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">p0</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">p1</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">p2</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="n">p</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">]</span>

<span class="n">calibrated_classifier</span> <span class="o">=</span> <span class="n">sig_clf</span><span class="o">.</span><span class="n">calibrated_classifiers_</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">prediction</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">calibrator</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">this_p</span><span class="p">)</span>
                        <span class="k">for</span> <span class="n">calibrator</span><span class="p">,</span> <span class="n">this_p</span> <span class="ow">in</span>
                        <span class="nb">zip</span><span class="p">(</span><span class="n">calibrated_classifier</span><span class="o">.</span><span class="n">calibrators_</span><span class="p">,</span> <span class="n">p</span><span class="o">.</span><span class="n">T</span><span class="p">)])</span><span class="o">.</span><span class="n">T</span>
<span class="n">prediction</span> <span class="o">/=</span> <span class="n">prediction</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span>

<span class="c1"># Plot modifications of calibrator</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">prediction</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
              <span class="n">prediction</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">prediction</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
              <span class="n">head_width</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">colors</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">])])</span>
<span class="c1"># Plot boundaries of unit simplex</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Simplex&quot;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]:</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">],</span> <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Illustration of sigmoid calibrator&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Probability class 1&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Probability class 2&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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